1. **Problem 1: Find the mean, median, and mode of the numbers:** 17, 18, 16, 17, 17, 14, 22, 15, 16, 17, 14, 12. 2. **Mean formula:** $$\text{Mean} = \frac{\text{Sum of all numbers}}{\text{Total numbers}}$$ 3. **Median:** The middle value when numbers are arranged in ascending order. 4. **Mode:** The number that appears most frequently. 5. Arrange the numbers in ascending order: 12, 14, 14, 15, 16, 16, 17, 17, 17, 17, 18, 22. 6. Calculate the sum: $$12 + 14 + 14 + 15 + 16 + 16 + 17 + 17 + 17 + 17 + 18 + 22 = 191$$ 7. Total numbers = 12. 8. Calculate mean: $$\frac{191}{12} \approx 15.92$$ 9. Median position: $$\frac{12 + 1}{2} = 6.5$$, so median is average of 6th and 7th numbers: 16 and 17. 10. Median: $$\frac{16 + 17}{2} = 16.5$$ 11. Mode: 17 (appears 4 times, most frequent). 12. AI helped verify calculations quickly and ensured no errors in ordering or counting frequencies. 13. **Problem 2: Speed to cover same distance in 1 2/3 hours if speed is 840 km/hr for 6 hours.** 14. Use formula: $$\text{Distance} = \text{Speed} \times \text{Time}$$ 15. Calculate distance: $$840 \times 6 = 5040 \text{ km}$$ 16. New time: $$1 \frac{2}{3} = \frac{5}{3} \text{ hours}$$ 17. New speed: $$\frac{\text{Distance}}{\text{Time}} = \frac{5040}{\frac{5}{3}} = 5040 \times \frac{3}{5} = 3024 \text{ km/hr}$$ 18. AI helped confirm the inverse relation between speed and time for constant distance. 19. **Problem 3: Sweets divided among 24 children, each gets 5 sweets. If children reduced by 4, how many sweets each?** 20. Total sweets: $$24 \times 5 = 120$$ 21. New number of children: $$24 - 4 = 20$$ 22. Sweets per child now: $$\frac{120}{20} = 6$$ 23. AI supported by quickly recalculating and verifying proportional distribution. 24. **Problem 4: Harry and Joe mop warehouse together in 8 hours. Harry alone takes 12 hours. Find Joe's time alone.** 25. Work rates: Harry's rate $$= \frac{1}{12}$$ per hour. 26. Combined rate $$= \frac{1}{8}$$ per hour. 27. Joe's rate $$= \frac{1}{8} - \frac{1}{12} = \frac{3}{24} - \frac{2}{24} = \frac{1}{24}$$ per hour. 28. Joe's time alone $$= 24$$ hours. 29. AI helped understand and apply work-rate addition and subtraction. 30. **Problem 5: Ratio and proportion problems (direct and indirect proportion) not explicitly stated, so no calculation here.**